tarek99 wrote:

anyone knows how option 1 is also suff.?

I dont think I would have initially guessed D. But spending about 7min on this in detail, I can see why D is the answer.

AB=OC=BO=OX=AX X is the midpoint of OA

So now we have two iscocoles triangles.

Lets name the angles with variables: OCB=y OBC=y BCO=z

BAO=x BOA=x ABO=w

(its obviously much easier to draw these)

S1: COD=60*

We need to write the appropriate eqautions out. 2y+z=180, 2x+w=180

y+w=180, Since we know COD=60* We know that x+z=120*

We have 4 equations and 4 unknowns. Should be enough. Lets solve anyway. We want to know what x=?

z=120-x 2y+120-x=180 --> 2y-x=60 x=2y-60.

w=180-2x --> y+180-2x=180--> y-2x=0 --> y=2x So x=2(2x)-60

-3x=-60 ---> x=20.

S2:

This one is very easy: we still have the same equations from above.

y+z=180, 2x+w=180, y+w=180

Since y=40* w=140* --> 2x=40* x=20*